The load might be oscillating. The issue maybe a mechanical thing. However as you have said that you already are using a shielded cable, try to use shielded twisted pair like CAT-6 cable. Also in the input section of the HX711 module try adding filter capacitor. Make sure power supply is clean and setup is away from a EM noise source.
Also as you said that you have used a mux (perhaps analog), have you compensated for voltage drop in mux by adding voltage buffer at the end of Mux output ? Please share diagram to enable us to help you further